= Metabolic intersection form of a four-dimensional product
A nontrivial product of positive-dimensional closed oriented <Witt spaces> of total dimension four has metabolic rational middle <intersection form>. For dimensions $1+3$, the two Künneth summands in degree two pair only with one another, so either is a half-dimensional isotropic subspace. For dimensions $2+2$, the outside degree-two summands pair with one another, and the $IH^1\otimes IH^1$ summand has the tensor pairing of two symplectic forms. A Lagrangian in the first symplectic factor tensored with the entire second factor is a half-dimensional isotropic subspace of that summand. Adding one outside summand gives a Lagrangian in the complete middle form. The <Witt bordism classification> then makes the product null-bordant.
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